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We use information from higher order moments to achieve identification of non-Gaussian structural vector autoregressive moving average (SVARMA) models, possibly nonfundamental or noncausal, through a frequency domain criterion based on higher order spectral densities. This allows us to identify the location of the roots of the determinantal lag matrix polynomials and to identify the rotation of the model errors leading to the structural shocks up to sign and permutation. We describe sufficient conditions for global and local parameter identification that rely on simple rank assumptions on the linear dynamics and on finite order serial and component independence conditions for the non-Gaussian structural innovations. We generalize previous univariate analysis to develop asymptotically normal and efficient estimates exploiting second and higher order cumulant dynamics given a particular structural shocks ordering without assumptions on causality or invertibility. Finite sample properties of estimates are explored with real and simulated data.

Identification and Estimation of Structural VARMA Models Using Higher Order Dynamics